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### Subject: sci.math FAQ: Master Mind

This article was archived around: 17 Feb 2000 22:55:52 GMT

Archive-name: sci-math-faq/mastermind
Last-modified: February 20, 1998
Version: 7.5

Master Mind
For the game of Master Mind it has been proven that no more than five
moves are required in the worst case.
One such algorithm was published in the Journal of Recreational
Mathematics; in '70 or '71 (I think), which always solved the 4 peg
problem in 5 moves. Knuth later published an algorithm which solves
the problem in a shorter number of moves - on average - but can take
six guesses on certain combinations.
In 1994, Kenji Koyama and Tony W. Lai found, by exhaustive search that
5625/1296 = 4.340 is the optimal strategy in the expected case. This
strategy may take six guesses in the worst case. A strategy that uses
at most five guesses in the worst case is also shown. This strategy
requires 5626/1296 = 4.341 guesses.
References
Donald E. Knuth. The Computer as Master Mind. J. Recreational
Mathematics, 9 (1976-77), 1-6.
Kenji Koyama, Tony W. Lai. An optimal Mastermind Strategy. J.
Recreational Mathematics, 1994.
--
Alex Lopez-Ortiz alopez-o@unb.ca
http://www.cs.unb.ca/~alopez-o Assistant Professor
Faculty of Computer Science University of New Brunswick